Collect and use element-frequency statistics for arrays.

This patch improves selectivity estimation for the array <@, &&, and @>
(containment and overlaps) operators.  It enables collection of statistics
about individual array element values by ANALYZE, and introduces
operator-specific estimators that use these stats.  In addition,
ScalarArrayOpExpr constructs of the forms "const = ANY/ALL (array_column)"
and "const <> ANY/ALL (array_column)" are estimated by treating them as
variants of the containment operators.

Since we still collect scalar-style stats about the array values as a
whole, the pg_stats view is expanded to show both these stats and the
array-style stats in separate columns.  This creates an incompatible change
in how stats for tsvector columns are displayed in pg_stats: the stats
about lexemes are now displayed in the array-related columns instead of the
original scalar-related columns.

There are a few loose ends here, notably that it'd be nice to be able to
suppress either the scalar-style stats or the array-element stats for
columns for which they're not useful.  But the patch is in good enough
shape to commit for wider testing.

Alexander Korotkov, reviewed by Noah Misch and Nathan Boley

8 files changed, 153 insertions, 122 deletions

diff --git a/src/include/catalog/catversion.h b/src/include/catalog/catversion.h
index 0335347155..223f157310 100644
--- a/src/include/catalog/catversion.h
+++ b/src/include/catalog/catversion.h
@@ -53,6 +53,6 @@
  */
 
 /*							yyyymmddN */
-#define CATALOG_VERSION_NO	201203021
+#define CATALOG_VERSION_NO	201203031
 
 #endif
diff --git a/src/include/catalog/pg_operator.h b/src/include/catalog/pg_operator.h
index ead5af6d80..48ddd16a94 100644
--- a/src/include/catalog/pg_operator.h
+++ b/src/include/catalog/pg_operator.h
@@ -1520,12 +1520,15 @@ DATA(insert OID = 2590 (  "|&>"    PGNSP PGUID b f f 718 718	16	 0	 0 circle_ove
 DESCR("overlaps or is above");
 
 /* overlap/contains/contained for arrays */
-DATA(insert OID = 2750 (  "&&"	   PGNSP PGUID b f f 2277 2277	16 2750  0 arrayoverlap areasel areajoinsel ));
+DATA(insert OID = 2750 (  "&&"	   PGNSP PGUID b f f 2277 2277	16 2750  0 arrayoverlap arraycontsel arraycontjoinsel ));
 DESCR("overlaps");
-DATA(insert OID = 2751 (  "@>"	   PGNSP PGUID b f f 2277 2277	16 2752  0 arraycontains contsel contjoinsel ));
+#define OID_ARRAY_OVERLAP_OP	2750
+DATA(insert OID = 2751 (  "@>"	   PGNSP PGUID b f f 2277 2277	16 2752  0 arraycontains arraycontsel arraycontjoinsel ));
 DESCR("contains");
-DATA(insert OID = 2752 (  "<@"	   PGNSP PGUID b f f 2277 2277	16 2751  0 arraycontained contsel contjoinsel ));
+#define OID_ARRAY_CONTAINS_OP	2751
+DATA(insert OID = 2752 (  "<@"	   PGNSP PGUID b f f 2277 2277	16 2751  0 arraycontained arraycontsel arraycontjoinsel ));
 DESCR("is contained by");
+#define OID_ARRAY_CONTAINED_OP	2752
 
 /* capturing operators to preserve pre-8.3 behavior of text concatenation */
 DATA(insert OID = 2779 (  "||"	   PGNSP PGUID b f f 25 2776	25	 0 0 textanycat - - ));
diff --git a/src/include/catalog/pg_proc.h b/src/include/catalog/pg_proc.h
index b476d47579..074051bdcc 100644
--- a/src/include/catalog/pg_proc.h
+++ b/src/include/catalog/pg_proc.h
@@ -869,6 +869,12 @@ DATA(insert OID = 2334 (  array_agg_finalfn   PGNSP PGUID 12 1 0 0 0 f f f f f f
 DESCR("aggregate final function");
 DATA(insert OID = 2335 (  array_agg		   PGNSP PGUID 12 1 0 0 0 t f f f f f i 1 0 2277 "2283" _null_ _null_ _null_ _null_ aggregate_dummy _null_ _null_ _null_ ));
 DESCR("concatenate aggregate input into an array");
+DATA(insert OID = 3816 (  array_typanalyze PGNSP PGUID 12 1 0 0 0 f f f f t f s 1 0 16 "2281" _null_ _null_ _null_ _null_ array_typanalyze _null_ _null_ _null_ ));
+DESCR("array typanalyze");
+DATA(insert OID = 3817 (  arraycontsel	   PGNSP PGUID 12 1 0 0 0 f f f f t f s 4 0 701 "2281 26 2281 23" _null_ _null_ _null_ _null_ arraycontsel _null_ _null_ _null_ ));
+DESCR("restriction selectivity for array-containment operators");
+DATA(insert OID = 3818 (  arraycontjoinsel PGNSP PGUID 12 1 0 0 0 f f f f t f s 5 0 701 "2281 26 2281 21 2281" _null_ _null_ _null_ _null_ arraycontjoinsel _null_ _null_ _null_ ));
+DESCR("join selectivity for array-containment operators");
 
 DATA(insert OID = 760 (  smgrin			   PGNSP PGUID 12 1 0 0 0 f f f f t f s 1 0 210 "2275" _null_ _null_ _null_ _null_	smgrin _null_ _null_ _null_ ));
 DESCR("I/O");
diff --git a/src/include/catalog/pg_statistic.h b/src/include/catalog/pg_statistic.h
index 0b15b001b4..383cc01415 100644
--- a/src/include/catalog/pg_statistic.h
+++ b/src/include/catalog/pg_statistic.h
@@ -21,16 +21,6 @@
 
 #include "catalog/genbki.h"
 
-/*
- * The CATALOG definition has to refer to the type of stavaluesN as
- * "anyarray" so that bootstrap mode recognizes it.  There is no real
- * typedef for that, however.  Since the fields are potentially-null and
- * therefore can't be accessed directly from C code, there is no particular
- * need for the C struct definition to show a valid field type --- instead
- * we just make it int.
- */
-#define anyarray int
-
 /* ----------------
  *		pg_statistic definition.  cpp turns this into
  *		typedef struct FormData_pg_statistic
@@ -83,7 +73,7 @@ CATALOG(pg_statistic,2619) BKI_WITHOUT_OIDS
 	 * we do not hard-wire any particular meaning for the remaining
 	 * statistical fields.	Instead, we provide several "slots" in which
 	 * statistical data can be placed.	Each slot includes:
-	 *		kind			integer code identifying kind of data
+	 *		kind			integer code identifying kind of data (see below)
 	 *		op				OID of associated operator, if needed
 	 *		numbers			float4 array (for statistical values)
 	 *		values			anyarray (for representations of data values)
@@ -98,40 +88,36 @@ CATALOG(pg_statistic,2619) BKI_WITHOUT_OIDS
 	int2		stakind2;
 	int2		stakind3;
 	int2		stakind4;
+	int2		stakind5;
 
 	Oid			staop1;
 	Oid			staop2;
 	Oid			staop3;
 	Oid			staop4;
+	Oid			staop5;
 
-	/*
-	 * THE REST OF THESE ARE VARIABLE LENGTH FIELDS, and may even be absent
-	 * (NULL). They cannot be accessed as C struct entries; you have to use
-	 * the full field access machinery (heap_getattr) for them.  We declare
-	 * them here for the catalog machinery.
-	 */
-
+#ifdef CATALOG_VARLEN			/* variable-length fields start here */
 	float4		stanumbers1[1];
 	float4		stanumbers2[1];
 	float4		stanumbers3[1];
 	float4		stanumbers4[1];
+	float4		stanumbers5[1];
 
-#ifdef CATALOG_VARLEN			/* variable-length fields start here */
 	/*
-	 * Values in these arrays are values of the column's data type.  We
-	 * presently have to cheat quite a bit to allow polymorphic arrays of this
-	 * kind, but perhaps someday it'll be a less bogus facility.
+	 * Values in these arrays are values of the column's data type, or of some
+	 * related type such as an array element type.  We presently have to cheat
+	 * quite a bit to allow polymorphic arrays of this kind, but perhaps
+	 * someday it'll be a less bogus facility.
 	 */
 	anyarray	stavalues1;
 	anyarray	stavalues2;
 	anyarray	stavalues3;
 	anyarray	stavalues4;
+	anyarray	stavalues5;
 #endif
 } FormData_pg_statistic;
 
-#define STATISTIC_NUM_SLOTS  4
-
-#undef anyarray
+#define STATISTIC_NUM_SLOTS  5
 
 
 /* ----------------
@@ -145,7 +131,7 @@ typedef FormData_pg_statistic *Form_pg_statistic;
  *		compiler constants for pg_statistic
  * ----------------
  */
-#define Natts_pg_statistic				22
+#define Natts_pg_statistic				26
 #define Anum_pg_statistic_starelid		1
 #define Anum_pg_statistic_staattnum		2
 #define Anum_pg_statistic_stainherit	3
@@ -156,22 +142,26 @@ typedef FormData_pg_statistic *Form_pg_statistic;
 #define Anum_pg_statistic_stakind2		8
 #define Anum_pg_statistic_stakind3		9
 #define Anum_pg_statistic_stakind4		10
-#define Anum_pg_statistic_staop1		11
-#define Anum_pg_statistic_staop2		12
-#define Anum_pg_statistic_staop3		13
-#define Anum_pg_statistic_staop4		14
-#define Anum_pg_statistic_stanumbers1	15
-#define Anum_pg_statistic_stanumbers2	16
-#define Anum_pg_statistic_stanumbers3	17
-#define Anum_pg_statistic_stanumbers4	18
-#define Anum_pg_statistic_stavalues1	19
-#define Anum_pg_statistic_stavalues2	20
-#define Anum_pg_statistic_stavalues3	21
-#define Anum_pg_statistic_stavalues4	22
+#define Anum_pg_statistic_stakind5		11
+#define Anum_pg_statistic_staop1		12
+#define Anum_pg_statistic_staop2		13
+#define Anum_pg_statistic_staop3		14
+#define Anum_pg_statistic_staop4		15
+#define Anum_pg_statistic_staop5		16
+#define Anum_pg_statistic_stanumbers1	17
+#define Anum_pg_statistic_stanumbers2	18
+#define Anum_pg_statistic_stanumbers3	19
+#define Anum_pg_statistic_stanumbers4	20
+#define Anum_pg_statistic_stanumbers5	21
+#define Anum_pg_statistic_stavalues1	22
+#define Anum_pg_statistic_stavalues2	23
+#define Anum_pg_statistic_stavalues3	24
+#define Anum_pg_statistic_stavalues4	25
+#define Anum_pg_statistic_stavalues5	26
 
 /*
- * Currently, three statistical slot "kinds" are defined: most common values,
- * histogram, and correlation.	Additional "kinds" will probably appear in
+ * Currently, five statistical slot "kinds" are defined by core PostgreSQL,
+ * as documented below.  Additional "kinds" will probably appear in
  * future to help cope with non-scalar datatypes.  Also, custom data types
  * can define their own "kind" codes by mutual agreement between a custom
  * typanalyze routine and the selectivity estimation functions of the type's
@@ -250,11 +240,14 @@ typedef FormData_pg_statistic *Form_pg_statistic;
  * the most common element values, and stanumbers their frequencies.  Unlike
  * MCV slots, frequencies are measured as the fraction of non-null rows the
  * element value appears in, not the frequency of all rows.  Also unlike
- * MCV slots, the values are sorted into order (to support binary search
- * for a particular value).  Since this puts the minimum and maximum
- * frequencies at unpredictable spots in stanumbers, there are two extra
- * members of stanumbers, holding copies of the minimum and maximum
- * frequencies.
+ * MCV slots, the values are sorted into the element type's default order
+ * (to support binary search for a particular value).  Since this puts the
+ * minimum and maximum frequencies at unpredictable spots in stanumbers,
+ * there are two extra members of stanumbers, holding copies of the minimum
+ * and maximum frequencies.  Optionally, there can be a third extra member,
+ * which holds the frequency of null elements (expressed in the same terms:
+ * the fraction of non-null rows that contain at least one null element).  If
+ * this member is omitted, the column is presumed to contain no null elements.
  *
  * Note: in current usage for tsvector columns, the stavalues elements are of
  * type text, even though their representation within tsvector is not
@@ -262,4 +255,17 @@ typedef FormData_pg_statistic *Form_pg_statistic;
  */
 #define STATISTIC_KIND_MCELEM  4
 
+/*
+ * A "distinct elements count histogram" slot describes the distribution of
+ * the number of distinct element values present in each row of an array-type
+ * column.  Only non-null rows are considered, and only non-null elements.
+ * staop contains the equality operator appropriate to the element type.
+ * stavalues is not used and should be NULL.  The last member of stanumbers is
+ * the average count of distinct element values over all non-null rows.  The
+ * preceding M (>=2) members form a histogram that divides the population of
+ * distinct-elements counts into M-1 bins of approximately equal population.
+ * The first of these is the minimum observed count, and the last the maximum.
+ */
+#define STATISTIC_KIND_DECHIST  5
+
 #endif   /* PG_STATISTIC_H */
diff --git a/src/include/catalog/pg_type.h b/src/include/catalog/pg_type.h
index e4bca55297..4e3bf69e6d 100644
--- a/src/include/catalog/pg_type.h
+++ b/src/include/catalog/pg_type.h
@@ -357,8 +357,8 @@ DATA(insert OID = 114 ( json		   PGNSP PGUID -1 f b U f t \054 0 0 199 json_in j
 DATA(insert OID = 142 ( xml		   PGNSP PGUID -1 f b U f t \054 0 0 143 xml_in xml_out xml_recv xml_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
 DESCR("XML content");
 #define XMLOID 142
-DATA(insert OID = 143 ( _xml	   PGNSP PGUID -1 f b A f t \054 0 142 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 199 ( _json	   PGNSP PGUID -1 f b A f t \054 0 114 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 143 ( _xml	   PGNSP PGUID -1 f b A f t \054 0 142 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 199 ( _json	   PGNSP PGUID -1 f b A f t \054 0 114 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
 
 DATA(insert OID = 194 ( pg_node_tree	PGNSP PGUID -1 f b S f t \054 0 0 0 pg_node_tree_in pg_node_tree_out pg_node_tree_recv pg_node_tree_send - - - i x f 0 -1 0 100 _null_ _null_ _null_ ));
 DESCR("string representing an internal node tree");
@@ -395,7 +395,7 @@ DESCR("geometric polygon '(pt1,...)'");
 DATA(insert OID = 628 (  line	   PGNSP PGUID 32 f b G f t \054 0 701 629 line_in line_out line_recv line_send - - - d p f 0 -1 0 0 _null_ _null_ _null_ ));
 DESCR("geometric line (not implemented)");
 #define LINEOID			628
-DATA(insert OID = 629 (  _line	   PGNSP PGUID	-1 f b A f t \054 0 628 0 array_in array_out array_recv array_send - - - d x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 629 (  _line	   PGNSP PGUID	-1 f b A f t \054 0 628 0 array_in array_out array_recv array_send - - array_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
 DESCR("");
 
 /* OIDS 700 - 799 */
@@ -422,11 +422,11 @@ DESCR("");
 DATA(insert OID = 718 (  circle    PGNSP PGUID	24 f b G f t \054 0 0 719 circle_in circle_out circle_recv circle_send - - - d p f 0 -1 0 0 _null_ _null_ _null_ ));
 DESCR("geometric circle '(center,radius)'");
 #define CIRCLEOID		718
-DATA(insert OID = 719 (  _circle   PGNSP PGUID	-1 f b A f t \054 0  718 0 array_in array_out array_recv array_send - - - d x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 719 (  _circle   PGNSP PGUID	-1 f b A f t \054 0  718 0 array_in array_out array_recv array_send - - array_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
 DATA(insert OID = 790 (  money	   PGNSP PGUID	 8 FLOAT8PASSBYVAL b N f t \054 0 0 791 cash_in cash_out cash_recv cash_send - - - d p f 0 -1 0 0 _null_ _null_ _null_ ));
 DESCR("monetary amounts, $d,ddd.cc");
 #define CASHOID 790
-DATA(insert OID = 791 (  _money    PGNSP PGUID	-1 f b A f t \054 0  790 0 array_in array_out array_recv array_send - - - d x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 791 (  _money    PGNSP PGUID	-1 f b A f t \054 0  790 0 array_in array_out array_recv array_send - - array_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
 
 /* OIDS 800 - 899 */
 DATA(insert OID = 829 ( macaddr    PGNSP PGUID	6 f b U f t \054 0 0 1040 macaddr_in macaddr_out macaddr_recv macaddr_send - - - i p f 0 -1 0 0 _null_ _null_ _null_ ));
@@ -442,44 +442,44 @@ DESCR("network IP address/netmask, network address");
 /* OIDS 900 - 999 */
 
 /* OIDS 1000 - 1099 */
-DATA(insert OID = 1000 (  _bool		 PGNSP PGUID -1 f b A f t \054 0	16 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1001 (  _bytea	 PGNSP PGUID -1 f b A f t \054 0	17 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1002 (  _char		 PGNSP PGUID -1 f b A f t \054 0	18 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1003 (  _name		 PGNSP PGUID -1 f b A f t \054 0	19 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1005 (  _int2		 PGNSP PGUID -1 f b A f t \054 0	21 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1006 (  _int2vector PGNSP PGUID -1 f b A f t \054 0	22 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1007 (  _int4		 PGNSP PGUID -1 f b A f t \054 0	23 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1000 (  _bool		 PGNSP PGUID -1 f b A f t \054 0	16 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1001 (  _bytea	 PGNSP PGUID -1 f b A f t \054 0	17 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1002 (  _char		 PGNSP PGUID -1 f b A f t \054 0	18 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1003 (  _name		 PGNSP PGUID -1 f b A f t \054 0	19 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1005 (  _int2		 PGNSP PGUID -1 f b A f t \054 0	21 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1006 (  _int2vector PGNSP PGUID -1 f b A f t \054 0	22 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1007 (  _int4		 PGNSP PGUID -1 f b A f t \054 0	23 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
 #define INT4ARRAYOID		1007
-DATA(insert OID = 1008 (  _regproc	 PGNSP PGUID -1 f b A f t \054 0	24 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1009 (  _text		 PGNSP PGUID -1 f b A f t \054 0	25 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 100 _null_ _null_ _null_ ));
+DATA(insert OID = 1008 (  _regproc	 PGNSP PGUID -1 f b A f t \054 0	24 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1009 (  _text		 PGNSP PGUID -1 f b A f t \054 0	25 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 100 _null_ _null_ _null_ ));
 #define TEXTARRAYOID		1009
-DATA(insert OID = 1028 (  _oid		 PGNSP PGUID -1 f b A f t \054 0	26 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1010 (  _tid		 PGNSP PGUID -1 f b A f t \054 0	27 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1011 (  _xid		 PGNSP PGUID -1 f b A f t \054 0	28 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1012 (  _cid		 PGNSP PGUID -1 f b A f t \054 0	29 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1013 (  _oidvector PGNSP PGUID -1 f b A f t \054 0	30 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1014 (  _bpchar	 PGNSP PGUID -1 f b A f t \054 0 1042 0 array_in array_out array_recv array_send bpchartypmodin bpchartypmodout - i x f 0 -1 0 100 _null_ _null_ _null_ ));
-DATA(insert OID = 1015 (  _varchar	 PGNSP PGUID -1 f b A f t \054 0 1043 0 array_in array_out array_recv array_send varchartypmodin varchartypmodout - i x f 0 -1 0 100 _null_ _null_ _null_ ));
-DATA(insert OID = 1016 (  _int8		 PGNSP PGUID -1 f b A f t \054 0	20 0 array_in array_out array_recv array_send - - - d x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1017 (  _point	 PGNSP PGUID -1 f b A f t \054 0 600 0 array_in array_out array_recv array_send - - - d x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1018 (  _lseg		 PGNSP PGUID -1 f b A f t \054 0 601 0 array_in array_out array_recv array_send - - - d x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1019 (  _path		 PGNSP PGUID -1 f b A f t \054 0 602 0 array_in array_out array_recv array_send - - - d x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1020 (  _box		 PGNSP PGUID -1 f b A f t \073 0 603 0 array_in array_out array_recv array_send - - - d x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1021 (  _float4	 PGNSP PGUID -1 f b A f t \054 0 700 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1028 (  _oid		 PGNSP PGUID -1 f b A f t \054 0	26 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1010 (  _tid		 PGNSP PGUID -1 f b A f t \054 0	27 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1011 (  _xid		 PGNSP PGUID -1 f b A f t \054 0	28 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1012 (  _cid		 PGNSP PGUID -1 f b A f t \054 0	29 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1013 (  _oidvector PGNSP PGUID -1 f b A f t \054 0	30 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1014 (  _bpchar	 PGNSP PGUID -1 f b A f t \054 0 1042 0 array_in array_out array_recv array_send bpchartypmodin bpchartypmodout array_typanalyze i x f 0 -1 0 100 _null_ _null_ _null_ ));
+DATA(insert OID = 1015 (  _varchar	 PGNSP PGUID -1 f b A f t \054 0 1043 0 array_in array_out array_recv array_send varchartypmodin varchartypmodout array_typanalyze i x f 0 -1 0 100 _null_ _null_ _null_ ));
+DATA(insert OID = 1016 (  _int8		 PGNSP PGUID -1 f b A f t \054 0	20 0 array_in array_out array_recv array_send - - array_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1017 (  _point	 PGNSP PGUID -1 f b A f t \054 0 600 0 array_in array_out array_recv array_send - - array_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1018 (  _lseg		 PGNSP PGUID -1 f b A f t \054 0 601 0 array_in array_out array_recv array_send - - array_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1019 (  _path		 PGNSP PGUID -1 f b A f t \054 0 602 0 array_in array_out array_recv array_send - - array_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1020 (  _box		 PGNSP PGUID -1 f b A f t \073 0 603 0 array_in array_out array_recv array_send - - array_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1021 (  _float4	 PGNSP PGUID -1 f b A f t \054 0 700 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
 #define FLOAT4ARRAYOID 1021
-DATA(insert OID = 1022 (  _float8	 PGNSP PGUID -1 f b A f t \054 0 701 0 array_in array_out array_recv array_send - - - d x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1023 (  _abstime	 PGNSP PGUID -1 f b A f t \054 0 702 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1024 (  _reltime	 PGNSP PGUID -1 f b A f t \054 0 703 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1025 (  _tinterval PGNSP PGUID -1 f b A f t \054 0 704 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1027 (  _polygon	 PGNSP PGUID -1 f b A f t \054 0 604 0 array_in array_out array_recv array_send - - - d x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1022 (  _float8	 PGNSP PGUID -1 f b A f t \054 0 701 0 array_in array_out array_recv array_send - - array_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1023 (  _abstime	 PGNSP PGUID -1 f b A f t \054 0 702 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1024 (  _reltime	 PGNSP PGUID -1 f b A f t \054 0 703 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1025 (  _tinterval PGNSP PGUID -1 f b A f t \054 0 704 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1027 (  _polygon	 PGNSP PGUID -1 f b A f t \054 0 604 0 array_in array_out array_recv array_send - - array_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
 DATA(insert OID = 1033 (  aclitem	 PGNSP PGUID 12 f b U f t \054 0 0 1034 aclitemin aclitemout - - - - - i p f 0 -1 0 0 _null_ _null_ _null_ ));
 DESCR("access control list");
 #define ACLITEMOID		1033
-DATA(insert OID = 1034 (  _aclitem	 PGNSP PGUID -1 f b A f t \054 0 1033 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1040 (  _macaddr	 PGNSP PGUID -1 f b A f t \054 0  829 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1041 (  _inet		 PGNSP PGUID -1 f b A f t \054 0  869 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 651  (  _cidr		 PGNSP PGUID -1 f b A f t \054 0  650 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1263 (  _cstring	 PGNSP PGUID -1 f b A f t \054 0 2275 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1034 (  _aclitem	 PGNSP PGUID -1 f b A f t \054 0 1033 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1040 (  _macaddr	 PGNSP PGUID -1 f b A f t \054 0  829 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1041 (  _inet		 PGNSP PGUID -1 f b A f t \054 0  869 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 651  (  _cidr		 PGNSP PGUID -1 f b A f t \054 0  650 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1263 (  _cstring	 PGNSP PGUID -1 f b A f t \054 0 2275 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
 #define CSTRINGARRAYOID		1263
 
 DATA(insert OID = 1042 ( bpchar		 PGNSP PGUID -1 f b S f t \054 0	0 1014 bpcharin bpcharout bpcharrecv bpcharsend bpchartypmodin bpchartypmodout - i x f 0 -1 0 100 _null_ _null_ _null_ ));
@@ -500,34 +500,34 @@ DESCR("time of day");
 DATA(insert OID = 1114 ( timestamp	 PGNSP PGUID	8 FLOAT8PASSBYVAL b D f t \054 0	0 1115 timestamp_in timestamp_out timestamp_recv timestamp_send timestamptypmodin timestamptypmodout - d p f 0 -1 0 0 _null_ _null_ _null_ ));
 DESCR("date and time");
 #define TIMESTAMPOID	1114
-DATA(insert OID = 1115 ( _timestamp  PGNSP PGUID	-1 f b A f t \054 0 1114 0 array_in array_out array_recv array_send timestamptypmodin timestamptypmodout - d x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1182 ( _date		 PGNSP PGUID	-1 f b A f t \054 0 1082 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 1183 ( _time		 PGNSP PGUID	-1 f b A f t \054 0 1083 0 array_in array_out array_recv array_send timetypmodin timetypmodout - d x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1115 ( _timestamp  PGNSP PGUID	-1 f b A f t \054 0 1114 0 array_in array_out array_recv array_send timestamptypmodin timestamptypmodout array_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1182 ( _date		 PGNSP PGUID	-1 f b A f t \054 0 1082 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1183 ( _time		 PGNSP PGUID	-1 f b A f t \054 0 1083 0 array_in array_out array_recv array_send timetypmodin timetypmodout array_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
 DATA(insert OID = 1184 ( timestamptz PGNSP PGUID	8 FLOAT8PASSBYVAL b D t t \054 0	0 1185 timestamptz_in timestamptz_out timestamptz_recv timestamptz_send timestamptztypmodin timestamptztypmodout - d p f 0 -1 0 0 _null_ _null_ _null_ ));
 DESCR("date and time with time zone");
 #define TIMESTAMPTZOID	1184
-DATA(insert OID = 1185 ( _timestamptz PGNSP PGUID -1 f b A f t \054 0	1184 0 array_in array_out array_recv array_send timestamptztypmodin timestamptztypmodout - d x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1185 ( _timestamptz PGNSP PGUID -1 f b A f t \054 0	1184 0 array_in array_out array_recv array_send timestamptztypmodin timestamptztypmodout array_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
 DATA(insert OID = 1186 ( interval	 PGNSP PGUID 16 f b T t t \054 0	0 1187 interval_in interval_out interval_recv interval_send intervaltypmodin intervaltypmodout - d p f 0 -1 0 0 _null_ _null_ _null_ ));
 DESCR("@ <number> <units>, time interval");
 #define INTERVALOID		1186
-DATA(insert OID = 1187 ( _interval	 PGNSP PGUID	-1 f b A f t \054 0 1186 0 array_in array_out array_recv array_send intervaltypmodin intervaltypmodout - d x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1187 ( _interval	 PGNSP PGUID	-1 f b A f t \054 0 1186 0 array_in array_out array_recv array_send intervaltypmodin intervaltypmodout array_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
 
 /* OIDS 1200 - 1299 */
-DATA(insert OID = 1231 (  _numeric	 PGNSP PGUID -1 f b A f t \054 0	1700 0 array_in array_out array_recv array_send numerictypmodin numerictypmodout - i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1231 (  _numeric	 PGNSP PGUID -1 f b A f t \054 0	1700 0 array_in array_out array_recv array_send numerictypmodin numerictypmodout array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
 DATA(insert OID = 1266 ( timetz		 PGNSP PGUID 12 f b D f t \054 0	0 1270 timetz_in timetz_out timetz_recv timetz_send timetztypmodin timetztypmodout - d p f 0 -1 0 0 _null_ _null_ _null_ ));
 DESCR("time of day with time zone");
 #define TIMETZOID		1266
-DATA(insert OID = 1270 ( _timetz	 PGNSP PGUID -1 f b A f t \054 0	1266 0 array_in array_out array_recv array_send timetztypmodin timetztypmodout - d x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1270 ( _timetz	 PGNSP PGUID -1 f b A f t \054 0	1266 0 array_in array_out array_recv array_send timetztypmodin timetztypmodout array_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
 
 /* OIDS 1500 - 1599 */
 DATA(insert OID = 1560 ( bit		 PGNSP PGUID -1 f b V f t \054 0	0 1561 bit_in bit_out bit_recv bit_send bittypmodin bittypmodout - i x f 0 -1 0 0 _null_ _null_ _null_ ));
 DESCR("fixed-length bit string");
 #define BITOID	 1560
-DATA(insert OID = 1561 ( _bit		 PGNSP PGUID -1 f b A f t \054 0	1560 0 array_in array_out array_recv array_send bittypmodin bittypmodout - i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1561 ( _bit		 PGNSP PGUID -1 f b A f t \054 0	1560 0 array_in array_out array_recv array_send bittypmodin bittypmodout array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
 DATA(insert OID = 1562 ( varbit		 PGNSP PGUID -1 f b V t t \054 0	0 1563 varbit_in varbit_out varbit_recv varbit_send varbittypmodin varbittypmodout - i x f 0 -1 0 0 _null_ _null_ _null_ ));
 DESCR("variable-length bit string");
 #define VARBITOID	  1562
-DATA(insert OID = 1563 ( _varbit	 PGNSP PGUID -1 f b A f t \054 0	1562 0 array_in array_out array_recv array_send varbittypmodin varbittypmodout - i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 1563 ( _varbit	 PGNSP PGUID -1 f b A f t \054 0	1562 0 array_in array_out array_recv array_send varbittypmodin varbittypmodout array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
 
 /* OIDS 1600 - 1699 */
 
@@ -541,7 +541,7 @@ DESCR("reference to cursor (portal name)");
 #define REFCURSOROID	1790
 
 /* OIDS 2200 - 2299 */
-DATA(insert OID = 2201 ( _refcursor    PGNSP PGUID -1 f b A f t \054 0 1790 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 2201 ( _refcursor    PGNSP PGUID -1 f b A f t \054 0 1790 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
 
 DATA(insert OID = 2202 ( regprocedure  PGNSP PGUID	4 t b N f t \054 0	 0 2207 regprocedurein regprocedureout regprocedurerecv regproceduresend - - - i p f 0 -1 0 0 _null_ _null_ _null_ ));
 DESCR("registered procedure (with args)");
@@ -563,17 +563,17 @@ DATA(insert OID = 2206 ( regtype	   PGNSP PGUID	4 t b N f t \054 0	 0 2211 regty
 DESCR("registered type");
 #define REGTYPEOID		2206
 
-DATA(insert OID = 2207 ( _regprocedure PGNSP PGUID -1 f b A f t \054 0 2202 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 2208 ( _regoper	   PGNSP PGUID -1 f b A f t \054 0 2203 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 2209 ( _regoperator  PGNSP PGUID -1 f b A f t \054 0 2204 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 2210 ( _regclass	   PGNSP PGUID -1 f b A f t \054 0 2205 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 2211 ( _regtype	   PGNSP PGUID -1 f b A f t \054 0 2206 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 2207 ( _regprocedure PGNSP PGUID -1 f b A f t \054 0 2202 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 2208 ( _regoper	   PGNSP PGUID -1 f b A f t \054 0 2203 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 2209 ( _regoperator  PGNSP PGUID -1 f b A f t \054 0 2204 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 2210 ( _regclass	   PGNSP PGUID -1 f b A f t \054 0 2205 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 2211 ( _regtype	   PGNSP PGUID -1 f b A f t \054 0 2206 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
 #define REGTYPEARRAYOID 2211
 
 /* uuid */
 DATA(insert OID = 2950 ( uuid			PGNSP PGUID 16 f b U f t \054 0 0 2951 uuid_in uuid_out uuid_recv uuid_send - - - c p f 0 -1 0 0 _null_ _null_ _null_ ));
 DESCR("UUID datatype");
-DATA(insert OID = 2951 ( _uuid			PGNSP PGUID -1 f b A f t \054 0 2950 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 2951 ( _uuid			PGNSP PGUID -1 f b A f t \054 0 2950 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
 
 /* text search */
 DATA(insert OID = 3614 ( tsvector		PGNSP PGUID -1 f b U f t \054 0 0 3643 tsvectorin tsvectorout tsvectorrecv tsvectorsend - - ts_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
@@ -592,36 +592,36 @@ DATA(insert OID = 3769 ( regdictionary	PGNSP PGUID 4 t b N f t \054 0 0 3770 reg
 DESCR("registered text search dictionary");
 #define REGDICTIONARYOID	3769
 
-DATA(insert OID = 3643 ( _tsvector		PGNSP PGUID -1 f b A f t \054 0 3614 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 3644 ( _gtsvector		PGNSP PGUID -1 f b A f t \054 0 3642 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 3645 ( _tsquery		PGNSP PGUID -1 f b A f t \054 0 3615 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 3735 ( _regconfig		PGNSP PGUID -1 f b A f t \054 0 3734 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
-DATA(insert OID = 3770 ( _regdictionary PGNSP PGUID -1 f b A f t \054 0 3769 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 3643 ( _tsvector		PGNSP PGUID -1 f b A f t \054 0 3614 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 3644 ( _gtsvector		PGNSP PGUID -1 f b A f t \054 0 3642 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 3645 ( _tsquery		PGNSP PGUID -1 f b A f t \054 0 3615 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 3735 ( _regconfig		PGNSP PGUID -1 f b A f t \054 0 3734 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 3770 ( _regdictionary PGNSP PGUID -1 f b A f t \054 0 3769 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
 
 DATA(insert OID = 2970 ( txid_snapshot	PGNSP PGUID -1 f b U f t \054 0 0 2949 txid_snapshot_in txid_snapshot_out txid_snapshot_recv txid_snapshot_send - - - d x f 0 -1 0 0 _null_ _null_ _null_ ));
 DESCR("txid snapshot");
-DATA(insert OID = 2949 ( _txid_snapshot PGNSP PGUID -1 f b A f t \054 0 2970 0 array_in array_out array_recv array_send - - - d x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 2949 ( _txid_snapshot PGNSP PGUID -1 f b A f t \054 0 2970 0 array_in array_out array_recv array_send - - array_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
 
 /* range types */
 DATA(insert OID = 3904 ( int4range		PGNSP PGUID  -1 f r R f t \054 0 0 3905 range_in range_out range_recv range_send - - range_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
 DESCR("range of integers");
 #define INT4RANGEOID		3904
-DATA(insert OID = 3905 ( _int4range		PGNSP PGUID  -1 f b A f t \054 0 3904 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 3905 ( _int4range		PGNSP PGUID  -1 f b A f t \054 0 3904 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
 DATA(insert OID = 3906 ( numrange		PGNSP PGUID  -1 f r R f t \054 0 0 3907 range_in range_out range_recv range_send - - range_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
 DESCR("range of numerics");
-DATA(insert OID = 3907 ( _numrange		PGNSP PGUID  -1 f b A f t \054 0 3906 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 3907 ( _numrange		PGNSP PGUID  -1 f b A f t \054 0 3906 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
 DATA(insert OID = 3908 ( tsrange		PGNSP PGUID  -1 f r R f t \054 0 0 3909 range_in range_out range_recv range_send - - range_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
 DESCR("range of timestamps without time zone");
-DATA(insert OID = 3909 ( _tsrange		PGNSP PGUID  -1 f b A f t \054 0 3908 0 array_in array_out array_recv array_send - - - d x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 3909 ( _tsrange		PGNSP PGUID  -1 f b A f t \054 0 3908 0 array_in array_out array_recv array_send - - array_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
 DATA(insert OID = 3910 ( tstzrange		PGNSP PGUID  -1 f r R f t \054 0 0 3911 range_in range_out range_recv range_send - - range_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
 DESCR("range of timestamps with time zone");
-DATA(insert OID = 3911 ( _tstzrange		PGNSP PGUID  -1 f b A f t \054 0 3910 0 array_in array_out array_recv array_send - - - d x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 3911 ( _tstzrange		PGNSP PGUID  -1 f b A f t \054 0 3910 0 array_in array_out array_recv array_send - - array_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
 DATA(insert OID = 3912 ( daterange		PGNSP PGUID  -1 f r R f t \054 0 0 3913 range_in range_out range_recv range_send - - range_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
 DESCR("range of dates");
-DATA(insert OID = 3913 ( _daterange		PGNSP PGUID  -1 f b A f t \054 0 3912 0 array_in array_out array_recv array_send - - - i x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 3913 ( _daterange		PGNSP PGUID  -1 f b A f t \054 0 3912 0 array_in array_out array_recv array_send - - array_typanalyze i x f 0 -1 0 0 _null_ _null_ _null_ ));
 DATA(insert OID = 3926 ( int8range		PGNSP PGUID  -1 f r R f t \054 0 0 3927 range_in range_out range_recv range_send - - range_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
 DESCR("range of bigints");
-DATA(insert OID = 3927 ( _int8range		PGNSP PGUID  -1 f b A f t \054 0 3926 0 array_in array_out array_recv array_send - - - d x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 3927 ( _int8range		PGNSP PGUID  -1 f b A f t \054 0 3926 0 array_in array_out array_recv array_send - - array_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
 
 /*
  * pseudo-types
@@ -638,7 +638,7 @@ DATA(insert OID = 3927 ( _int8range		PGNSP PGUID  -1 f b A f t \054 0 3926 0 arr
  */
 DATA(insert OID = 2249 ( record			PGNSP PGUID -1 f p P f t \054 0 0 2287 record_in record_out record_recv record_send - - - d x f 0 -1 0 0 _null_ _null_ _null_ ));
 #define RECORDOID		2249
-DATA(insert OID = 2287 ( _record		PGNSP PGUID -1 f p P f t \054 0 2249 0 array_in array_out array_recv array_send - - - d x f 0 -1 0 0 _null_ _null_ _null_ ));
+DATA(insert OID = 2287 ( _record		PGNSP PGUID -1 f p P f t \054 0 2249 0 array_in array_out array_recv array_send - - array_typanalyze d x f 0 -1 0 0 _null_ _null_ _null_ ));
 #define RECORDARRAYOID	2287
 DATA(insert OID = 2275 ( cstring		PGNSP PGUID -2 f p P f t \054 0 0 1263 cstring_in cstring_out cstring_recv cstring_send - - - c p f 0 -1 0 0 _null_ _null_ _null_ ));
 #define CSTRINGOID		2275
diff --git a/src/include/commands/vacuum.h b/src/include/commands/vacuum.h
index 4526648a4f..3deee66b41 100644
--- a/src/include/commands/vacuum.h
+++ b/src/include/commands/vacuum.h
@@ -61,6 +61,11 @@ typedef struct VacAttrStats *VacAttrStatsP;
 typedef Datum (*AnalyzeAttrFetchFunc) (VacAttrStatsP stats, int rownum,
 												   bool *isNull);
 
+typedef void (*AnalyzeAttrComputeStatsFunc) (VacAttrStatsP stats,
+											 AnalyzeAttrFetchFunc fetchfunc,
+											 int samplerows,
+											 double totalrows);
+
 typedef struct VacAttrStats
 {
 	/*
@@ -83,10 +88,7 @@ typedef struct VacAttrStats
 	 * These fields must be filled in by the typanalyze routine, unless it
 	 * returns FALSE.
 	 */
-	void		(*compute_stats) (VacAttrStatsP stats,
-											  AnalyzeAttrFetchFunc fetchfunc,
-											  int samplerows,
-											  double totalrows);
+	AnalyzeAttrComputeStatsFunc compute_stats;	/* function pointer */
 	int			minrows;		/* Minimum # of rows wanted for stats */
 	void	   *extra_data;		/* for extra type-specific data */
 
@@ -167,5 +169,6 @@ extern void lazy_vacuum_rel(Relation onerel, VacuumStmt *vacstmt,
 /* in commands/analyze.c */
 extern void analyze_rel(Oid relid, VacuumStmt *vacstmt,
 			BufferAccessStrategy bstrategy);
+extern bool std_typanalyze(VacAttrStats *stats);
 
 #endif   /* VACUUM_H */
diff --git a/src/include/utils/array.h b/src/include/utils/array.h
index c6d0ad67f8..1da20fefda 100644
--- a/src/include/utils/array.h
+++ b/src/include/utils/array.h
@@ -289,4 +289,9 @@ extern ArrayType *create_singleton_array(FunctionCallInfo fcinfo,
 extern Datum array_agg_transfn(PG_FUNCTION_ARGS);
 extern Datum array_agg_finalfn(PG_FUNCTION_ARGS);
 
+/*
+ * prototypes for functions defined in array_typanalyze.c
+ */
+extern Datum array_typanalyze(PG_FUNCTION_ARGS);
+
 #endif   /* ARRAY_H */
diff --git a/src/include/utils/selfuncs.h b/src/include/utils/selfuncs.h
index bffc2d80ef..4529f27683 100644
--- a/src/include/utils/selfuncs.h
+++ b/src/include/utils/selfuncs.h
@@ -95,9 +95,6 @@ typedef enum
 	Pattern_Prefix_None, Pattern_Prefix_Partial, Pattern_Prefix_Exact
 } Pattern_Prefix_Status;
 
-
-/* selfuncs.c */
-
 /* Hooks for plugins to get control when we ask for stats */
 typedef bool (*get_relation_stats_hook_type) (PlannerInfo *root,
 														  RangeTblEntry *rte,
@@ -110,6 +107,8 @@ typedef bool (*get_index_stats_hook_type) (PlannerInfo *root,
 												  VariableStatData *vardata);
 extern PGDLLIMPORT get_index_stats_hook_type get_index_stats_hook;
 
+/* Functions in selfuncs.c */
+
 extern void examine_variable(PlannerInfo *root, Node *node, int varRelid,
 				 VariableStatData *vardata);
 extern bool get_restriction_variable(PlannerInfo *root, List *args,
@@ -197,4 +196,13 @@ extern Datum gistcostestimate(PG_FUNCTION_ARGS);
 extern Datum spgcostestimate(PG_FUNCTION_ARGS);
 extern Datum gincostestimate(PG_FUNCTION_ARGS);
 
+/* Functions in array_selfuncs.c */
+
+extern Selectivity scalararraysel_containment(PlannerInfo *root,
+						   Node *leftop, Node *rightop,
+						   Oid elemtype, bool isEquality, bool useOr,
+						   int varRelid);
+extern Datum arraycontsel(PG_FUNCTION_ARGS);
+extern Datum arraycontjoinsel(PG_FUNCTION_ARGS);
+
 #endif   /* SELFUNCS_H */